2D far-field observations

A number of observations about the 2D far-field expansion can be made.

• It is rather fortuitous that the airfoil quantities which are of the most interest for engineering — lift, drag, moment, area and thickness — are also the quantities which are needed to estimate the velocity field far from the airfoil.

• All the Vff terms in (2.79) after Vo decay to zero with increasing distance r, so very far away we have Vff ~ Vo as expected. However, for moderate distances from the airfoil, the far-field terms give a much better approximation to the actual V.

• The various far-field terms in (2.79) after Vo have different rates of decay with distance. The Л and Г terms decay as 1/r, while the kx and kz doublet terms decay as 1/r2. In practice this means that at sufficiently large distances, the doublet terms can be dropped from the expansion with little loss in accuracy. Conversely, when sufficiently close to the airfoil the doublet terms may very well dominate. [1]